Finite Group Databasebeta

D17×#2044 #17062080

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD17×#2044

Splittings

FittingC17×#2044 ⋊ C2
SylowC17 ⋊ C2×#2044

Subgroups

subgroupG/H
centerC22#120×D17
commutator, cosocleC24×C17C24
FrattiniC24C23×D17
FittingC17×#2044C2
socleC22×C17C2×#120
prime radicalD17×#534C2
hypercenter#2044D17
hypocenterC17C2×#2044
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #2044

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 197324);